Operators on Banach lattices and the Radon-Nikodým theorem
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- by William Feldman PDF
- Proc. Amer. Math. Soc. 100 (1987), 517-521 Request permission
Abstract:
For positive operators between Banach lattices a concept of absolute continuity is considered. On an AM-space with order unit norm, $S$ is shown to be absolutely continuous with respect to $T$ if and only if there is an approximation of $S$ by finite sums of operators of the type $q \circ T \circ h$ where $h$ and $q$ are multiplication operators or orthomorphisms. Given $T$ compact, compactness of $S$ is characterized.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 517-521
- MSC: Primary 47B55; Secondary 46B30
- DOI: https://doi.org/10.1090/S0002-9939-1987-0891156-9
- MathSciNet review: 891156